A marine biologist is investigating the growth rates of coral fragments using a new mineral supplement. Eight coral fragments are each split into two halves; one half is treated with the supplement, and the other serves as a control. The biologist claims that the mean growth of the treated fragments is more than 1.2 mm greater than the mean growth of the control fragments over a six-month period. The recorded growths (in mm) are shown in the table below:
| Fragment | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Control (CCC) | 12.4 | 15.1 | 11.8 | 14.2 | 13.5 | 12.9 | 14.8 | 13.0 |
| Treated (TTT) | 14.5 | 16.9 | 14.3 | 17.4 | 14.9 | 15.1 | 16.7 | 15.9 |
Assuming that the differences in growth are normally distributed, test the biologist's claim at the 1% significance level. State your hypotheses clearly and show your working.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.